Re: infinity

Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
> stephen@xxxxxxxxxx said:
>> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
>> > stephen@xxxxxxxxxx said:
>> >> I do not think that matters. Suppose that
>> >> F = sum S^k for all not imponderably enormous k
>> >> and that F is not imponderably enormous.
>> >>
>> >> Then
>> >> F = F + (sum S^k for all not imponderably enormous k <> F)
>> >>
>> >> Presumably if F is not imponderably enormous than we can
>> >> safely substract it from both sides. So
>> >> 0 = (sum S^k for all not imponderably enormous k <> F)
>> >>
>> >> Well 1,2,3, etc are all not imponderably enormous, and
>> >> S^1 + S^2 + S^3 > 0
>> >> for S>0.
>> >>
>> >> Tony is basically claiming that "finite" numbers exist
>> >> that are greater than the sum of all "finite" numbers,
>> >> including themselves. This is going to be problematic
>> >> for whatever definition of "finite" you plug in.
>> >>
>> >> Stephen
>> >>
>> > I am claiming no such thing. You are the one supposing a largest finite in your
>> > stuff above, hence the contradiction. I never claimed to have any number for
>> > the sum of all finite numbers.
>>
>> You claimed that the sum of all finite numbers was finite.
>> Is the sum of all finite numbers somehow finite, but it is
>> not a number? With you I suppose anything is possible.
>>
>> Stephen
>>
> Is the largest finite finite, but not a number? Answer your own questions for
> once.

The largest finite does not exist. Therefore it is not finite.
Just as the smallest even prime larger than 2 is not even,
nor is it prime, nor is it larger than 2.

> I have already shown that the largest finite natural and the size of the
> set of finite naturals are one and the same number. Does one exist while the
> other doesn't?

You have not shown that. You proved that all cats were grey
and then concluded that your dog was grey. Your argument
was:
all sets of the form { 1, 2, ... n} have a largest
member n, and the size of the set is n

the set { 1, 2, 3, .... } does not have a largest member

therefore the size of { 1, 2, 3, ... } equals its largest member

That looks a lot like

all cats are grey

rover is a dog

therefore rover is grey

Anyway, you now seem to at least recognize that a largest finite
is critical to all of your arguments as you lately have been
defending the existence of the largest finite. I am not sure if
that is progress or not.

Stephen
.